The authors of a paper compared two different instruments for measuring a person's capacity for breathing out air. (This measurement is helpful in diagnosing various lung disorders.) The two instruments considered were a Wright peak flow meter and a mini-Wright peak flow meter. Seventeen people participated in the study, and for each person air flow was measured once using the Wright meter and once using the mini-Wright meter. The Wright meter is thought to provide a better measure of air flow, but the mini-Wright meter is easier to transport and to use. Use of the mini-Wright meter could be recommended as long as there is not convincing evidence that the mean reading for the mini-Wright meter is different from the mean reading for Wright meter. For purposes of this exercise, you can assume that it is reasonable to consider the 17 people who participated in this study as representative of the population of interest. Data values from this paper are given in the accompanying table. Subject Mini Wright Meter Wright Meter 1 517 494 2 430 395 3 520 516 4 428 434 5 500 476 6 600 557 7 364 413 8 380 442 9 658 650 10 442 433 11 432 417 12 626 656 13 260 267 14 477 478 15 259 178 16 350 423 17 451 422 Use the given data to determine if there is convincing evidence that the mean reading differs for the two instruments. (Use ?d = ?mini-Wright − ?Wright.) Find the test statistic. (Round your answer to two decimal places.) t = Find the df. (Round your answer down to the nearest whole number.) df = Use technology to find the P-value. (Round your answer to four decimal places.) P-value =

Big Ideas Math A Bridge To Success Algebra 1: Student Edition 2015

1st Edition

ISBN:9781680331141

Author:HOUGHTON MIFFLIN HARCOURT

Publisher:HOUGHTON MIFFLIN HARCOURT

Chapter4: Writing Linear Equations

Section: Chapter Questions

Problem 14CR

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Question

The authors of a paper compared two different instruments for measuring a person's capacity for breathing out air. (This measurement is helpful in diagnosing various lung disorders.) The two instruments considered were a Wright peak flow meter and a mini-Wright peak flow meter. Seventeen people participated in the study, and for each person air flow was measured once using the Wright meter and once using the mini-Wright meter.

The Wright meter is thought to provide a better measure of air flow, but the mini-Wright meter is easier to transport and to use. Use of the mini-Wright meter could be recommended as long as there is not convincing evidence that the mean reading for the mini-Wright meter is different from the mean reading for Wright meter. For purposes of this exercise, you can assume that it is reasonable to consider the 17 people who participated in this study as representative of the population of interest. Data values from this paper are given in the accompanying table.

Subject	Mini Wright Meter	Wright Meter
1	517	494
2	430	395
3	520	516
4	428	434
5	500	476
6	600	557
7	364	413
8	380	442
9	658	650
10	442	433
11	432	417
12	626	656
13	260	267
14	477	478
15	259	178
16	350	423
17	451	422

Use the given data to determine if there is convincing evidence that the mean reading differs for the two instruments. (Use ?_d = ?_mini-Wright − ?_Wright.)

Find the test statistic. (Round your answer to two decimal places.)

t =

Find the df. (Round your answer down to the nearest whole number.)

df =

Use technology to find the P-value. (Round your answer to four decimal places.)

P-value =

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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Subject	Mini Wright Meter	Wright Meter
1	517	494
2	430	395
3	520	516
4	428	434
5	500	476
6	600	557
7	364	413
8	380	442
9	658	650
10	442	433
11	432	417
12	626	656
13	260	267
14	477	478
15	259	178
16	350	423
17	451	422

Subject	Mini Wright Meter	Wright Meter
1	517	494
2	430	395
3	520	516
4	428	434
5	500	476
6	600	557
7	364	413
8	380	442
9	658	650
10	442	433
11	432	417
12	626	656
13	260	267
14	477	478
15	259	178
16	350	423
17	451	422

Subject	Mini Wright Meter	Wright Meter
1	517	494
2	430	395
3	520	516
4	428	434
5	500	476
6	600	557
7	364	413
8	380	442
9	658	650
10	442	433
11	432	417
12	626	656
13	260	267
14	477	478
15	259	178
16	350	423
17	451	422